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Method of generating uniform and independent random numbers

A random number, uniform technology, applied in the direction of random number generator, electrical digital data processing, digital data processing parts, etc.

Inactive Publication Date: 2015-01-14
中泽宏 +1
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Nakazawa and Nakazawa (2012a,b) found a breakthrough in the puzzle using patterns formed by the product of two odd prime powers

Method used

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  • Method of generating uniform and independent random numbers
  • Method of generating uniform and independent random numbers
  • Method of generating uniform and independent random numbers

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Embodiment Construction

[0044] Detailed description of the first invention

[0045] To avoid ambiguity in this specification, multiply the sequence {n,nz,nz 2 ,···} is considered to be an infinite sequence at first, and there is no equality relation modulo d. The corresponding random numbers are regenerated as:

[0046] v 1 =r 0 / d, r 0 =n, 10

[0047] v k =r k-1 / d, r k ≡nz k mod(d), 1k

[0048] We start with a second-degree spectral test, taking consecutive 2-tuples in the generated sequence. Define the vector Q k :=(nz k-1 , nz k )=nz k-1 (1,z). Let Q k ' denotes an arbitrary integer vector with a value equal to Q k The coordinates of these results modulo d. Understand that Q k ' is obtained from the vector Q by translating along the coordinate axis by some integer multiple of d k get. Along the second axis, d is translated by adding the vector e 2 :=(0, d) to take effect. A d translation along the first axis is achieved by adding e 1 ':=d(1,z)-z(0,d)=d(...

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Abstract

An invention is presented with new and simple ways of spectral tests applicable to the multiplicative congruential generator (d,z) with any odd modulus d and any multiplier z coprime to d. The invention realizes powerful ways to select multipliers of excellence with greatly improved statistical performances in their generation of uniform and independent random numbers. Related two inventions for new designs of the generator (d,z) are presented at the same time, as strongly facilitative for the application of advocated extended spectral tests, by exploiting specific structures of moduluses formed by two odd-prime-powers so as to realize improved periodic structures that are set conveniently out of tune avoiding harmful resonances.

Description

technical field [0001] Kronecker said: God created the natural numbers, the others are the credit of human beings. The inventor thinks he means the whole of mathematics is based on God inventing the natural numbers or inventing the recurrence relation x k+1 =x k +1 where x 1 =1; and the efforts, inspirations, and ideas of outstanding people later gave us rational numbers, real numbers, complex numbers, matrices, geometry, analysis, and algebra. The inventors are far from understanding the depth and state of beauty of mathematics today. But the prospect of building entire mathematical systems on top of the simplest recurrence relations motivates us. We work on generating random numbers on a computer. In particular, we found that any sequence of uniform and irrelevant random numbers on the computer can be regarded as generated by means of multiplication and congruence, and this fact is taken as the basis of the technical method of random number generation. Hope we have not...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F7/58
CPCG06F7/588G06F7/586
Inventor 中泽宏中泽直也
Owner 中泽宏